How do I make a weapon shoot at the center of the screen?
You can use a bit of Python to get started, without knowing your exact implementation of the weapon system, i can't give you the full code.

# get vector from centre of screen
cam = logic.getCurrentScene().active_camera
# vector in world space
vect = cam.getScreenVect(0.5, 0.5)
# get length of vect
length = -cam.position[2]/vect[2]
p = vect * length
# position of p (somewhat ahead of camera)
pos = cam.position + p


With that, you should be able to either ray cast the bullet, or have it go toward that direction.